Zirakzigil (sometimes abbreviated to simply Zirak) is the Dwarvish name for this mountain, meaning something like 'silver spike', referring to an extremely narrow and pointed summit. The name was formed into Elvish as Celebdil, and in Mannish tongues it was rendered as 'Silvertine'.
On the narrow peak of Zirakzigil was a single tower, Durin's Tower, reached by the Endless Stair that led up from the deepest depths below Moria through the rock of the mountain itself. It was at the summit of Zirakzigil that Gandalf fought a Balrog in the Battle of the Peak, a dreadful confrontation that shattered the ancient tower and broke the mountainside itself.
In the first edition of The Lord of the Rings the name of this mountain is consistently hyphenated as 'Zirak-zigil'. For the second printing, Tolkien chose to amend this to an unhyphenated form, correcting the name throughout to 'Zirakzigil', except for two cases which he apparently overlooked. Later editions have been further corrected to use the unhyphenated form in all cases.
Zigil is known to be the Dwarvish word for 'silver', but the meaning of zirak is uncertain. Mannishtine refers to a high point or peak; it is probably a fair assumption that the Khuzdul word has a similar meaning. Zirak does appear in one other place, as a title or surname of Gamil the teacher of Telchar, so it probably carries the more general meaning of 'high' or 'tall'.